Ciliary Stretch-dependent Changes in The Surface Profiles of the Human Crystalline Lens during Dis-Accommodation using Finite Element Method

Abstract

 

Purpose:

 

Investigations into accommodation have used lens stretchers and computational models. As an initial step to reconcile responses seen in ex vivo lens stretching studies (e.g. Manns et al, 2008) we constructed a finite element (FE) model to analyse the stretch-dependent changes in lens shape with particular focus on surface profiles.

 

Methods:

 

An axisymmetric, non-homogeneous, non-linear FEM of a 29-yo lens based on the model of Burd et al (2002) was constructed. Stretching was effected by displacing the zonules attachment point radially to 0.49 mm in 12 steps ranging in size from 0.039 mm to 0.061 mm. Coordinates for the anterior and posterior capsule, cortex and nucleus profiles were extracted at each step. Functions (see figure) relating sagittal height (h) to radial distance (r) from axis (6^th-order even polynomial) and ciliary stretch (s; 4^th-order polynomial) for each of the six profiles was computed using multiple regression. Interaction terms involving combinations of orders of S and R were included. Functions were confined to the central 5 mm of the lens.

 

Results:

 

Increase in diameter (D) and concomitant decrease in thickness (T) with s are described by D (mm)=-0.153*s²+1.67*s+8.63 (RMSE < 0.4 mm), T (mm)= -0.500*s³+ 1.25*s²-2.21*s+4.13 (RMSE < 0.2 mm). Optical power (P) versus stretch is described by P (D)=-27.8*x³+44.4*x²-40.8*x+12.5. Statistically significant (p < 0.05) coefficients for the functions for the outer lens and nucleus surfaces are given in the figure with a plot of h vs r and s for the anterior lens.Only interaction terms with 2^nd-order in r were significant, suggesting accommodation does not introduce significant spherical aberration-like changes to the lens’ surfaces.

 

Conclusions:

 

Stretch-dependent mathematical functions for the profile of lens surfaces have been derived using FE modelling. These functions may provide a basis for analytical solutions for the optics of accommodation.  

 

Keywords: accommodation • computational modeling